Integration of the unknow variable

Question

Jamal Ahmad 2013-10-11

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https://ww2.mathworks.cn/matlabcentral/answers/89934-integration-of-the-unknow-variable

评论： sixwwwwww 2013-10-11

Hi, Is it possible in MatLab to integrate a function of the unkow variable? for example:

clc; clear all; close all;
syms a b f g x
f = erfc(sqrt((x)/2))*(1./g)*exp(-(x/g));
g = int(f,0,inf,x);

How I can do this integration?

Thank you

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Answer 1

Sean de Wolski 2013-10-11

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You have the inputs to int backwards:

G = int(f,x,0,inf)

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Jamal Ahmad 2013-10-11

Thank you very much for the answer. But I have this warning:

Warning: Explicit integral could not be found.

Sean de Wolski 2013-10-11

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This implies that there is not an explicit integral for this. Instead, you might want to consider calculating the integral numerically using integral

doc integral

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Answer 2

sixwwwwww 2013-10-11

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Dear Jamal Ahmad, You are using "int" in wrong format. See http://www.mathworks.com/help/symbolic/int.html

g = int(f,0,inf,x);

It should be used in its proper form with proper sequence of input arguments as:

int(expr,var,a,b)

So the corrected code is:

syms f g x 
f = erfc(sqrt((x)/2))*(1./g)*exp(-(x/g)); 
Integration_result = int(f,x,0,Inf)

Here arguments x, 0 and Inf are placed rightly. Good luck!

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sixwwwwww 2013-10-11

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Basically, error functions is like other functions so it can be integrated in the same way as other functions are integrated. I have integrated your function and got the following result using the code given above in my ans.

Integration_result = int((exp(-x/g)*erfc((x/2)^(1/2)))/g, x == 0..Inf)

So the integration is already performed. It did get any numerical value as result because we don't know the value of symbol "g". Now if you replace g with some numeric value then you will get the integration result. For example, if you replace "g" with value 2 then you can get numerical result. I hope it ans your question. If you need code doing this then let me know I will post it

sixwwwwww 2013-10-11

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Dear Jamal, for your convenience here is the final code:

syms f g x % Your symbolic variables
f = erfc(sqrt((x)/2))*(1./g)*exp(-(x/g)); % Your function to be integrated
f_new = subs(f, g, 2); % replacing "g" with value 2 in function "f"
Integration_result = double(int(f_new,x,0,Inf)) % Getting final integration ans

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